The flop call by villian basically eliminates 2 hands:
1) air - no heart
2) low flush

Once he min/raises the turn, I think he must have the Ah. Either nut flush, AhKx, or AhAx. I guess he could just decide that you never have a heart and play KK like this, but that would be... odd. KK I think is raising the flop big.

I think your play is good because what flush hand is he 3-betting pre-flop? AQh? Possible he is that aggro, but at 50NL, I think you have to assume a tight 3-bet range until otherwise demonstrated.

So shoving here is fine, because he is probably drawing to 8 outs (10 if he has AA)